The present paper follows the computational approach to 3-manifold classification via edge-coloured graphs, already performed in [1] (with respect to orientable 3-manifolds up to 28 coloured tetrahedra), in [2] (with respect to non-orientable3-manifolds up to 26 coloured tetrahedra), in [3] and [4] (with respect to genus two 3-manifolds up to 34 coloured tetrahedra): in fact, by automatic generation and analysis of suitable edge-coloured graphs, called crystallizations, we obtain a catalogue of all orientable 3-manifolds admitting coloured triangulations with 30 tetrahedra. These manifolds are unambiguously identified via JSJ decompositions and fibering structures. It is worth noting that, in the present work, a suitable use of elementary combinatorial moves yields an automatic partition of the elements of the generated crystallization catalogue into equivalence classes, which turn out to be in one-to one correspondence with the homeomorphism classes of the represented manifolds.

A catalogue of orientable 3-manifolds triangulated by 30 coloured tetrahedra / Casali, Maria Rita; Cristofori, Paola. - In: JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS. - ISSN 0218-2165. - STAMPA. - 17:5(2008), pp. 579-599. [10.1142/S0218216508006312]

A catalogue of orientable 3-manifolds triangulated by 30 coloured tetrahedra

CASALI, Maria Rita;CRISTOFORI, Paola
2008

Abstract

The present paper follows the computational approach to 3-manifold classification via edge-coloured graphs, already performed in [1] (with respect to orientable 3-manifolds up to 28 coloured tetrahedra), in [2] (with respect to non-orientable3-manifolds up to 26 coloured tetrahedra), in [3] and [4] (with respect to genus two 3-manifolds up to 34 coloured tetrahedra): in fact, by automatic generation and analysis of suitable edge-coloured graphs, called crystallizations, we obtain a catalogue of all orientable 3-manifolds admitting coloured triangulations with 30 tetrahedra. These manifolds are unambiguously identified via JSJ decompositions and fibering structures. It is worth noting that, in the present work, a suitable use of elementary combinatorial moves yields an automatic partition of the elements of the generated crystallization catalogue into equivalence classes, which turn out to be in one-to one correspondence with the homeomorphism classes of the represented manifolds.
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579
599
A catalogue of orientable 3-manifolds triangulated by 30 coloured tetrahedra / Casali, Maria Rita; Cristofori, Paola. - In: JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS. - ISSN 0218-2165. - STAMPA. - 17:5(2008), pp. 579-599. [10.1142/S0218216508006312]
Casali, Maria Rita; Cristofori, Paola
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/583988
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